Date of Graduation

1994

Document Type

Dissertation/Thesis

Abstract

Prior calculations of heat transfer coefficients for an experimental horizontal tube in a bubbling fluidized bed have assumed that the heat conduction through the tube wall is one dimensional. However, a comparison between one dimensional (1D) and two dimensional (2D) analyses and comparing them with experimental data shows that there exists a significant difference between 1D and 2D calculations. The analysis was accomplished by solving the unsteady 1D and 2D heat conduction equation across the tube wall numerically. The boundary conditions were taken from the temperature data measured at five different locations around the horizontal tube simultaneously. A correction factor has been developed to correct the errors in heat transfer coefficients arising from the 1D approach. Analytical solutions were also developed by modeling the tube wall composed of steady state and unsteady state regions. The present 1D and 2D analysis as well as the present analytical approach are utilized in the context of interpreting the experimental data better. However, they could also be used as predictive tools. A rigorous grid dependence test was applied, and it was shown that the results, in particular the heat flux, are very sensitive to the grid size and distribution. Therefore, to achieve better grid convergence when heat flux is sought, the discretization error in the heat flux rather than in the temperature calculations is considered. This should be done even in cases where temperature is the primary unknown, because it is usually the derivative of temperature which is of any physical importance. The errors were also strongly dependent on the number of iterations, which need to be increased as the grid is refined. The present application showed that a nonuniform grid refinement throughout the calculation domain gives a more efficient (less expensive) solution than uniform grid refinement. Furthermore, for calculation of the temperature gradient at the wall, a parabolic profile assumption gave a faster grid convergence compared to a linear profile assumption. The local instantaneous temperature, heat transfer coefficient, and differential pressure data, gathered around a horizontal tube in a fluidized bed, have been analyzed by using deterministic chaos theory. The mutual information function (MIF) has been applied to the signals to observe the relationship between points separated in time. MIF was also used to provide the most appropriate time delay constant {dollar}\au{dollar} to reconstruct an m-dimensional phase portrait of the one dimensional time series. The distinct variation of MIF around the tube indicates the variations of solid-surface contact in the circumferential direction. The correlation coefficient was evaluated to calculate the correlation dimension, which provides an indication of the local fractal nature of the system. The correlation exponent is a measure of dimension of the strange attractor. The Kolmogorov entropies of the signals were approximated by using the correlation coefficient. Kolmogorov entropy considers the inherent multi-dimensional nature of chaotic data. A positive estimation of Kolmogorov entropy is an indication of chaotic nature of the signal. The Kolmogorov entropies of the temperature data around the tube were found to be between 10 bits/sec and 20 bits/sec. A comparison between the signals has shown that the local instantaneous heat transfer coefficient exhibits higher degree of chaos than the local temperature and differential pressure signals.

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